Steps for Factoring Quadratic Expressions

Steps for Factoring Quadratic Expressions

1. Does the expression have a Greatest Common Factor?

   • Yes
     • Find the GCF and divide the terms by it. Then, write the GCF infront and bracket the remaining divided terms,
   • No
     • Is the expression structured like this: a^2 x^2 - b^2
       • Yes
         • This is Difference of Squares. You square root the following terms that can come out as a positive or negative number and put them in the structure: (ax - b) (ax + b)
       • No
         • Is the expression structured like this: a^2x^2 + or - 2abx + b^2
           • Yes
             • This is Perfect Squares. You square root the following terms that can come out as only a positive number. After square rooting, you simplify the expression.
           • No
             • Is the expression structured like this: x^2 + bx + c
               • Yes
                 • This is a Difference Trinomial we will use Product/Sum method. First, we multiply the first and last term, then we figure the terms that multiply into the term that was multiplied by the first and last term but also add to the middle term. Then we break down the middle term, replacing it with the terms that we found. We then split the expression in two, finding the GCF for both. Once done, we put the coefficients together and the terms in a bracket to form another expression which is our answer.
               • No
                 • Is the expression structured like this: ax^2 + bx +c
                   • This is a Complex Trinomial, we will use Decomposistion. First we find two numbers that add to bx and multiply to c. Then we decompose the middle term to the terms we found. Then we factor out the GCF. Then We then split the expression in two and put the coefficients together and the terms in a bracket to form another expression which is our answer.